Conventionally, in vehicles, there is known, as a technique for reducing fuel consumption during traveling, inertia traveling for causing a vehicle to travel by inertia by disconnecting the power transmission between an engine and driving wheels during traveling. The controller disconnects the power transmission between the engine and the driving wheels by releasing a clutch in an engaged state interposed therebetween during normal traveling and causes the vehicle to shift to the inertia traveling. Further, when the inertia travelling is returned to the normal traveling, the controller engages the clutch in the released state. For example, Patent Literatures 1 and 2 described below disclose a technique as to the inertia traveling. Further, Patent Literature 3 described below discloses a technique for prohibiting the gear shift control of a transmission when the engine side rotating speed of a clutch exceeds a predetermined rotating speed during an inertia control.